I would like to use sed to search for the first part of a text file with consecutive lines with at least n non-space characters. I would like to print from the first of those lines to the end of the file.

I know you said sed (no pun intended) but if you can live with PERL, the following should do what you want (n=20):

#!/usr/bin/perl -w
my $n=20; ## The minimum length of the line
my $prev=""; ## This holds the number of chars in the previous line
my $pline; ## This holds the previous line
my $pp=0; ## Counter, lines will be printed if set to 1
while(<>){
## Skip line processing if we have already
## found our lines of interest
$pp==1 && do {print; next};
## Get non-space chars
my $a=join("",/[^\s]+/g);
## Print if requirements are met.
if (length($prev)> $n && length($a)> $n){
print $pline,$_;
$pp=1;
}
$prev=$a;
$pline=$_;
}